{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NUR7DPX4VKEFD5COEFABUBOHTR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6fbe5374f2c32ad02a48b9d713926e977f6b02816f02b7adf7ba21ce1e788b15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-01T16:32:19Z","title_canon_sha256":"6655f8653d8e3df595e6fdb78437b2247ab3adb923bedcd8b4fea8c64f1f34f2"},"schema_version":"1.0","source":{"id":"2209.00571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00571","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00571v1","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00571","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_12","alias_value":"NUR7DPX4VKEF","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_16","alias_value":"NUR7DPX4VKEFD5CO","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_8","alias_value":"NUR7DPX4","created_at":"2026-07-05T04:53:51Z"}],"graph_snapshots":[{"event_id":"sha256:e369e8da339b00ec7a8ec0a718b440dd0b67b0e716c68b6f40e9cac2ccb71082","target":"graph","created_at":"2026-07-05T04:53:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.00571/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that for each property $\\mathsf{P}\\in \\{\\mathsf{OP}, \\mathsf{IP}, \\mathsf{TP}_1, \\mathsf{TP}_2, \\mathsf{ATP}, \\mathsf{SOP}_3\\}$ there is a poset $\\Sigma_{\\mathsf{P}}$ such that a theory has property $\\mathsf{P}$ if and only if some model interprets a poset in which $\\Sigma_{\\mathsf{P}}$ can be embedded. We also introduce a new property $\\mathsf{SUP}$, consistent with $\\mathsf{NIP}_2$ and implying $\\mathsf{ATP}$ and $\\mathsf{SOP}$.","authors_text":"Dar\\'io Garc\\'ia, Rosario Mennuni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-01T16:32:19Z","title":"Model-theoretic dividing lines via posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00571","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4c2ee315e787c1c4d279988cf5556a676387987ce981917dc49321f6562b061f","target":"record","created_at":"2026-07-05T04:53:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6fbe5374f2c32ad02a48b9d713926e977f6b02816f02b7adf7ba21ce1e788b15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-01T16:32:19Z","title_canon_sha256":"6655f8653d8e3df595e6fdb78437b2247ab3adb923bedcd8b4fea8c64f1f34f2"},"schema_version":"1.0","source":{"id":"2209.00571","kind":"arxiv","version":1}},"canonical_sha256":"6d23f1befcaa8851f44e21401a05c79c65a84e832fddde073970348397b99280","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d23f1befcaa8851f44e21401a05c79c65a84e832fddde073970348397b99280","first_computed_at":"2026-07-05T04:53:51.552334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:53:51.552334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jyQxCx2+urUbpvmDll5ykB4Eafu1dbd3Ee2/H0QPC9Yjej3XgbGi3mi/KnXa22GDpnLsvrZGI4W7oVuAv/PjBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:53:51.552741Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.00571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c2ee315e787c1c4d279988cf5556a676387987ce981917dc49321f6562b061f","sha256:e369e8da339b00ec7a8ec0a718b440dd0b67b0e716c68b6f40e9cac2ccb71082"],"state_sha256":"fb126acfae79bc74e4c24474655283f8de0cc57ed9f05e6ac1c6cebee48a603a"}